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hal-00129728, version 1

On the topology defined by Thurston's asymmetric metric

Athanase Papadopoulos 1, Guillaume Théret 1

(06/07/2006)

Résumé : In this paper, we establish some properties of Thurston's asymmetric metric L on the Teichmueller space T of a surface with negative Euler characteristic. We study convergence of sequences of elements in T in the sense of L, as well as sequences that tend to infinity in T. We show that the topology that the asymmetric metric induces on Teichmueller space is the same as the usual topology. Furthermore, we show that L satisfies the axioms of a (not necessarily symmetric) metric in the sense of Busemann and conclude that L is complete in the sense of Busemann.

  • 1 :  Institut de Recherche Mathématique Avancée (IRMA)
  • CNRS : UMR7501 – Université Louis Pasteur - Strasbourg I
  • Domaine : Mathématiques/Variables complexes
  • Mots-clés : "Teichmueller space – Thurston's asymmetric metric – geodesic lamination"
 
  • hal-00129728, version 1
  • http://hal.archives-ouvertes.fr/hal-00129728
  • oai:hal.archives-ouvertes.fr:hal-00129728
  • Contributeur : Véronique Bertrand <>
  • Soumis le : Jeudi 8 Février 2007, 15:09:25
  • Dernière modification le : Jeudi 8 Février 2007, 17:07:28